PROBLEMS
OF UNIVERSITY ENTRANCE EXAMINATION OF BUSINESS ECONOMICS
3^{rd} PART  TOPIC 9. (You must do mainly those in bold)
2.01_03 – 2.02_03 – 2.03_03 – 2.04_03 – 2.05_03 – 2.06_03 – 2.07_03 – 2.08_03 – 2.09_03 – 2.10_03 – 2.11_03 – 2.12_03 – 2.13_03 – 2.14_03 – 2.15_03 – 2.16_03 – 2.17_03 – 2.18_03 – 2.19_03 – 2.01_04 – 2.02_04 – 2.03_04 – 2.01_05 – 2.02_05 – 2.03_05 – 2.04_05 – 2.05_05 – 2.06_05 – 2.01_06 – 2.02_06 – 2.03_06 – 2.04_06 – 2.05_06 – 2.06_06 – 2.01_07 – 2.02_07 – 2.03_07 – 2.04_07 – 2.01_08 – 2.02_08 – 2.03_08 – 2.04_08 – 2.05_08 – 2.06_08 – 2.01_09 – 2.02_09 – 2.03_09 – 2.04_09 – 2.05_09
PR_2.01_03. The firm MEGA, Ltd. is studying three investments. The initial outlay and the cash flows of each investment in euros appear in the table. Determine which one would be the best investment to the firm according to the criteria of the Net Present Value or NPV. Consider an annual interest rate of 7%. OUTCOMES: NPV_{X} = 12,088.13€, NPV_{Y} = 9,364.74€, NPV_{Z} = 3,985.75€ SOL_PR_2.01_03
Project 
Initial outlay 
Q1 
Q2 
Q3 
Q4 
X 
18,000 
7,000 
9,000 
8,000 
12,000 
Y 
30,000 
15,000 
15,000 
15,000 
 
Z 
25,000 
12,000 
11,000 
10,000 
 
PR_2.02_03. The firm WERBEL sells bicycles and it's thinking about the possibility of expanding its business towards the sale of clothes and complements used to do cycling. In order to that it has planned an outlay of 600,000 ptas. and the following collections and payments. Determine if the investment is interesting to the firm OUTCOMES: PB = xy, 8 m and 28 d. NPV = 74,393.68€ SOL_PR_2.02_03
YEARS 
COLLECTIONS 
PAYMENTS 
1 
100,000 
50,000 
2 
200,000 
60,000 
3 
300,000 
65,000 
4 
300,000 
65,000 
According to the criteria of the Payback, knowing that the minimum demanded period of time is five years
According to the criteria of the Net Present Value, if the interest rate is 8%
PR_2.03_03. The Manufactures of the Bay's manager wants to improve the productivity of his firm, therefore, he wants to know the firm's cash conversion cycle before of the beginning of the program of improving. Calculate the information that the manager needs related to the cash conversion cycle if the data are the following (averages of the period and in million of pesetas): OUTCOMES: RMp = 23.53 days, GPp = 8.33 days, FGp = 20.86 days, Rp = 20.86 days, CCC = 73.58 days SOL_PR_2.03_03
ITEMS 
AMOUNTS 
Sales cost 
2,012 
Total cost of production 
2,104 
Average raw material stock 
63 
Average finished goods stock 
115 
Material purchases 
977 
Total sales 
2,415 
Average goods in process stock 
48 
Average receivables stock 
138 
PR_2.04_03. Determine the more profitable choice to an investor who is offered the following possibilities to make a certain investment, according to the criteria of the Net Preset Value (NPV) if the interest rate is 7%: OUTCOMES: NPV_{A} =  207,647€; NPV_{B} =  103,697; NPV_{C} = 185,716€ SOL_PR_2.04_03

Initial Outlay 
Net Cash Flow 1^{st} Year 
Net Cash Flow 2^{nd} Year 
Net Cash Flow 3^{rd} Year 
Net Cash Flow 4^{th} Year 
Net Cash Flow 5^{th} Year 
Project A 
1,000,000 
100,000 
150,000 
200,000 
250,000 
300,000 
Project B 
1,500,000 
200,000 
300,000 
350,000 
400,000 
500,000 
Project C 
1,700,000 
400,000 
600,000 
300,000 
600,000 
400,000 
PR_2.05_03. The data related to three projects of investment that a firm wants to evaluate are in the attached table. If the interest rate is 6%: OUTCOMES: NPV_{A} = 5,768,343.06€; NPV_{B} = 1,318,898.21€; NPV_{C} = 3,558,576.88€, PB_{A} = x y and 8 m, PB_{B} = x y and 3 m, PB_{C} = x y, 10 m and 15 d SOL_PR_2.05_03
Put in order the aforementioned investments according to their order of preference
By usin the criteria of Net Present Value (NPV)
By using the criteria of Payback
Comment the outcome
Projects 
Initial Outlay 
Net Cash Flow 1^{st} Year 
Net Cash Flow 2^{nd} Year 
Net Cash Flow 3^{rd} Year 
Net Cash Flow 4^{th} Year 
Net Cash Flow 5^{th} Year 
A 
10,000,000 
0 
0 
6,000,000 
6,000,000 
8,000,000 
B 
20,000,000 
3,000,000 
4,000,000 
5,000,000 
6,000,000 
8,000,000 
C 
16,000,000 
4,000,000 
5,000,000 
8,000,000 
3,000,000 
3,000,000 
PR_2.06_03. If the annual interest rate is 8%: OUTCOMES: NPV_{A} = 3,829,086.43; NPV_{B} = 3,524,416.59; NPV_{C} = 2,587,894.88; PB_{A} = x y and 10 m, PB_{B} = x y and 9 m, PB_{C} = x y, 10 m and 15 d SOL_PR_2.06_03
Put in order the investments according to the order of preference
By using the criteria of Net Present Value (NPV)
By using the criteria of Payback
Initial Outlay 
Net Cash Flow 1^{st} Year 
Net Cash Flow 2^{nd} Year 
Net Cash Flow 3^{rd} Year 
Net Cash Flow 4^{th} Year 
Net Cash Flow 5^{th} Year 
project A 10,000,000 
1,000,000 
2,000,000 
6,000,000 
6,000,000 
8,000,000 
project B 18,000,000 
3,000,000 
4,000,000 
5,000,000 
6,000,000 
8,000,000 
project C 16,000,000 
4,000,000 
5,000,000 
8,000,000 
3,000,000 
3,000,000 
PR_2.07_03. We want to know which of the following two investments is preferable according to the Payback and to the Net Present Value (NPV). The annual interes rate is 10%. Is there an agreement between both criteria? Comment the outcomes and reason the answer OUTCOMES: PB_{A} = x y; PB_{B} = x y; NPV_{A} = 5,849.50; NPV_{B} = 11,789.50 SOL_PR_2.07_03

Investment A 
Investment B 
Initial outlay 
10,000 
10,000 
1^{st} Cash Flow 
5,000 
2,000 
2^{nd} Cash Flow 
5,000 
4,000 
3^{rd} Cash Flow 
5,000 
4,000 
4^{th} Cash Flow 
5,000 
20,000 
PR_2.08_03. The firm PLAVAN Ltd. is thinking about two possible projects of investment. Determine the Payback and the Net Present Value of each one of the investments. The annual interest rate is 10%. Is there an agreement between both criteria in order to establish which one is the best option to the firm? Reason your answer OUTCOMES: NPV_{A} = 2,787.37; NPV_{B} = 1,113.44; PB_{A} = x y and 3 m; PB_{B} = x y SOL_PR_2.08_03

Initial outlay 
Cash Flow 1^{st} Year 
Cash Flow 2^{nd} Year 
Cash Flow 3^{rd} Year 
Project A 
10,000 
2,000 
6,000 
8,000 
Project B 
8,000 
3,000 
5,000 
3,000 
PR_2.09_03. The corporation QQQ has a Share Capital of 73,647€ divided in 4,900 shares. The shares of the aforementioned corporation quote in the Stock Market at 165% and the expected annual dividends are 2.40€. The annual interes rate is 7%. Calculate the nominal value, the market value and the theoretical value of the shares of the corporation QQQ OUTCOMES: NV = 15.03 €/share; MV = 24.80 €/share; TV = 34.29 €/share SOL_PR_2.09_03
PR_2.10_03. PERFUMASA is planning to make a new investment, in order to that, it has several options: either to diversify towards another line of products or to expand the existing line. The data for the study of the profitability of the investment appear in the following table (in euros). Help you to decide which investment would you prefer and why according to the criteria of Net Present Value and Payback. The annual interest rate is 7%. OUTCOMES: NPV_{D} = 15,430.37, NPV_{E} = 79,458.96, PB_{D} = x y, PB_{E} = x y, 3 m and 18 d SOL_PR_2.10_03

Initial outlay 
Collectins 1^{st} Year 
Payments 1^{st} year 
Collections 2^{nd} Year 
Payments 2^{nd} Year 
Collections 3^{rd} Year 
Payments 3^{rd} Year 
Diversification 
90,000 
50,000 
60,000 
140,000 
100,000 
150,000 
90,000 
Expansion 
78,000 
180,000 
120,000 
180,000 
120,000 
180,000 
120,000 
PR_2.11_03. A project of investment had an initial outlay of 100,000€ and the cash flows of the first and second years were 40,000 and 30,000€, respectively. Calculate the cash flow of the third year, if the Payback of the investment was 2 years and 9 months OUTCOME: x = 40,000€ SOL_PR_2.11_03
PR_2.12_03. A building firm with 120,000€ of Share Capital made up of 300 shares, has obtained a distributing profit of 12,000€ at the end of the year and it has created reserves of 24,000€. Determine: OUTCOMES: NV = 400€; TV = 480€; DIV = 40€; Net worth = 144,000€ SOL_PR_2.12_03
The nominal value of the shares
The theoretical value of each share
The distributed dividend per share
The Net worth
PR_2.13_03. Obtain the Net Present Value of an investment with an useful life of 5 years, which initial outlay is 1,500 m.u. that are paid in only one time and that have the following collections and payments (in m.u.). The annual interest rate is 5%. OUTCOME: NPV = 292.85 m.u. SOL_PR_2.13_03
YEARS 
COLLECTIONS 
PAYMENTS 
1 
600 
300 
2 
700 
400 
3 
1,000 
500 
4 
1,000 
500 
5 
1,000 
500 
PR_2.14_03. You have the data in monetary units related to three projects of investment that a firm wants to evaluate in the attached table. If the annual interest rate is 6.5%. OUTCOMES: NPV_{A} = 9,163.35€; NPV_{B} = 2,380.57€; NPV_{C} = 5,998.32€; PB_{A} = x y and 10 m, PB_{B} = x y, 9 m and 18 d, PB_{C} = x y, 8 m and 17 d SOL_PR_2.14_03
Put in order of preference the investments by using the criteria of Net Present Value (NPV)
Put in order of preference the investments by using the criteria of Payback,
INITIAL OUTLAY 
NET CASH FLOWS 

1^{st} Year 
2^{nd} Year 
3^{rd} Year 
4^{th} Year 

PROJECT A 25,000 
0 
0 
30,000 
12,000 
PROJECT B 20,000 
5,000 
2,000 
15,000 
15,000 
PROJECT C 16,000 
5,000 
6,000 
7,000 
8,000 
PR_2.15_03. A firm is studying two projects of investment; A and B. Project A means an initial outlay of one million of euros and it's expected to obtain, each one of the five years that it will last, a net cash flow of 300,000€. Project B means an initial outlay of one million euros, as well, but the net cash flows are: 150,000€ 1^{st} year, 250,000€ 2^{nd} year, 450,000 3^{rd} year, 400,000 4^{th} year and 350,000 5^{th} year. If the annual interest rate is 5%, determine which investment is the best, by evaluating them using the NPV method. OUTCOMES: NPV_{A} = 298,843€ and NPV_{B} = 361,656.58€ SOL_PR_2.15_03
PR_2.16_03. WE'VE GOT ANOTHER PROBLEM LIKE THIS ONE
PR_2.17_03. It's equal to 2.12_03 SOL_PR_2.17_03
PR_2.18_03. An investment is offered the two following possibilities to make a certain project. Determine the more profitable option, according to the criteria of Net Present Value (NPV) if the interest rate is 8% and according to the Payback. OUTCOMES: NPV_{A} = 691.6€; NPV_{B} =  1,620.17€; PB_{A} = x y and 10 m; PB_{B} = x y and 6 m SOL_PR_2.18_03
PROJECT A 
PROJECT B 


Collections € 
Payments € 

Collections € 
Payments € 
Initial outlay 

10,000 
Initial outlay 

14,100 
1^{st} year 
4,000 
2,000 
1^{st} year 
6,000 
3,000 
2^{nd} year 
5,000 
2,500 
2^{nd} year 
6,800 
3,400 
3^{rd} year 
8,000 
5,000 
3^{rd} year 
8,200 
5,000 
4^{th} year 
6,000 
3,000 
4^{th} year 
7,000 
4,000 
5^{th} year 
5,600 
2,500 
5^{th} year 
8,000 
5,000 
PR_2.19_03. The firm “Babe Apples” markets apple trees to nurseries. Its Share Capital is divided in 50,000 shares of 1,000 m.u. each one. The firm quotes in the Stock Market at 1,256 m.u./share and it has reserves of 10,000,000 m.u. OUTCOMES: SC = 50,000,000 m.u.; QUOTE . . . PAR, TV = 1,200 m.u. SOL_PR_2.19_03
Calculate the amount of the Share Capital
Determine if the shares quote under par, over par or at par
Calculate the theoretical value of each share
PR_2.01_04. A firm has the following information about two projects of investment. a) Which of the two investments is preferable according to the criteria of Payback? and b) Which investment is more profitable? Comment the outcome. OUTCOMES: PB_{1} = x y and 10 m; PB_{2} = x y and 14 d SOL_PR_2.01_04

Investment 1 
Investment 2 
Initial outlay 
1,500 
1,500 
Cash flow of the 1^{st} period 
1,000 
100 
Cash flow of the 2^{nd} period 
600 
1,000 
Cash flow of the 3^{rd} period 
0 
10,000 
PR_2.02_04. A firm plans to make a project of investment to acquire a machine valued in 13,000€. The project lasts four years. The planned revenue for each year with the acquisition of this new machine are: 6,000€; 12,000€; 12,500€ and 20,000€ respectively. The planned operating expenses appear in the following table. The interes rate is 15%; the salvage value is zero and the tax on profits is 25%. You must decide if the investment is a good idea for the firm or not, according to the Net Present Value (NPV). OUTCOME: NPV = 9,888.6€ SOL_PR_2.02_04
EXPENSES 
1^{st} year 
2^{nd} year 
3^{rd} year 
4^{th} year 
Labour 
600 
630 
750 
800 
Raw material 
300 
300 
400 
400 
General expenses 
150 
200 
200 
150 
PR_2.03_04. A firm is thinking about to acquire a machine with an useful life of 4 years. The investment means to pay initially 3,000€ and 1,000€ each one of the years, the planned collections are 2,000€ each year. If the salvage value of the machine is 200€ and the interest rate is 5%. Calculate the NPV of the investment. OUTCOME: NPV = 710.49€ SOL_PR_2.03_04
PR_2.01_05. A firm has two alternative projects of investment. Calculate the NPV, knowing that the interest rate is 4%, and reason which investment would interest to make. RESULTADOS: VAN_{X} = 16.605,83, VAN_{Y} = 16.750,9 SOL_PR_2.01_05
Project 
Initial outlay 
1^{st} year 
2^{nd} year 
3^{rd} year 

Collections 
Payments 
Collections 
Payments 
Collections 
Payments 

X 
11,000 
12,000 
4,000 
15,000 
5,000 
18,000 
6,000 
Y 
11,000 
15,000 
5,000 
17,000 
7,000 
20,000 
10,000 
PR_2.02_05. If we have the projects of investment that appear in the attached table, and, if the annual interest rate is 8%: OUTCOMES: NPV_{A} = 427.78 m.u.; NPV_{B} = 308.39 m.u.; NPV_{C} = 759.79 m.u.; PB_{A} = x y, 8 m and 10 d; PB_{B} = x y and 6 m; PB_{C} = x y and 8 m SOL_PR_2.02_05
Projects 
Initial outlay (m.u.) 
Net Cash Flow 1^{st} year (m.u.) 
Net Cash Flow 2^{nd} year (m.u.) 
Net Cash Flow 3^{rd} year (m.u.) 
A 
10,000 
7,500 
3,600 
500 
B 
10,000 
4,000 
4,000 
4,000 
C 
10,000 
0 
8,000 
3,000 
Indicate which is the best project of investment according to the Net Present Value (NPV)
Calculate the Payback of each one of these projects, considering that the cash flows are obtained in an uniform way along the year. According to this criteria, which project will be the best to the firm?
PR_2.03_05. A firm has the chance of invest in one of these three projects: OUTCOMES: PB_{1} = x y and 8 m; PB_{2} = x y, 8 m and 23 d; PB_{3} = x y, 8 m and 22 d, NPV_{1} = 5,219.85€; NPV_{2} = 5,328.19€; NPV_{3} = 6,473.82€ SOL_PR_2.03_05
Projects 
Initial outlay 
Net Cash flows 

1^{st} year 
2^{nd} year 
3^{rd} year 

P1 
80,000 
 
50,000 
45,000 
P2 
90,000 
52,000 
 
52,000 
P3 
80,000 
40,000 
 
55,000 
According to the Payback, which is the best investment? Consider that the cash flows are obtained in an uniform way along the year
According to the Net Present Value (NPV), which is the best investment, if the annual interest rate is 4.5%?
PR_2.04_05. A firm's chief financial officer asks for your collaboration to evaluate the advisability of each one of the three projects of investment that appear in the following table. According to the chief officer, project A is the best option for the firm. Calculate the Payback of each investment and indicate if your opinion is the same as the chief financial officer. Consider that the net cash flows are obtained in an uniform way along the year. OUTCOMES: PB_{A} = x y, 7 m and 15 d; PB_{B} = x y, 11 m and 12 d; PB_{C} = x y, 11 m and 4 d SOL_PR_2.04_05
PROJECTS 
INITIAL OUTLAY 
NET CASH FLOWS 

1^{st} year 
2^{nd} year 
3^{rd} year 
4^{th} year 

A 
18,000 
6,000 
7,000 
8,000 
9,000 
B 
15,000 
3,000 
1,000 
0 
20,000 
C 
13,000 
0 
0 
14,000 
10,000 
PR_2.05_05. A firm has three choices of investment, that mean an initial outlay and ones net cash flows that appear in the following table. If we suposse an annual interest rate of 4%, put in order from the highest to the lower profitability these investments, by using the criteria of: OUTCOMES: NPV_{A} = 18,210.98; NPV_{B} = 11,558.26; NPV_{C} = 8,880.32; PB_{A} = x y, 1 m and 6 d; PB_{B} = x y and 23 d; PB_{C} = x y and 3 m SOL_PR_2.05_05
Projects of investment 
Initial outlay 
Net cash flows 

1^{st} year 
2^{nd} year 
3^{rd} year 
4^{th} year 

Investment A 
20,000 
10,000 
8,000 
20,000 
4,000 
Investment B 
27,000 
8,000 
18,000 
16,000 
0 
Investment C 
8,000 
6,000 
1,000 
12,000 
1,600 
Net Present Value (NPV)
Payback, considering that the cash flows are obtained in an uniform way along the year
PR_2.06_05. Investments A and B have the following characteristics: OUTCOMES: PB_{A} = x y, 9 m and 18 d; PB_{B} = x y and 3 m; NPV_{A} = 194.32; NPV_{B} = 11,295.78 SOL_PR_2.06_05

Investment A 
Investment B 
Initial outlay 
10,000 
10,000 
Net cash flow of the 1^{st} period 
6,000 
1,000 
Net Cash Flow of the 2^{nd} period 
5,000 
4,000 
Net Cash Flow of the 3^{rd} period 
100 
20,000 
According to the Payback, which investment is preferable? Calculate the payback of both investments considering that the cash flows are obtained in an uniform way along the year
According to the NPV, which investment is preferable? (consider an interest rate of 6%) Explain the differences with the outcomes of point a)
PR_2.01_06. The firm OO's chief financial officer, is studying the posibility of expanding the factory, in order to that, three projects have been presented. The temporal analysis of these investments is in the following (data in million of m.u.): OUTCOMES: NPV_{A} = 15.19; NPV_{B} = 81.1; NPV_{C} = 83.2; PB_{A} = x y, 2 m and 20 d; PB_{B} = x y; PB_{C} = x y SOL_PR_2.01_06
NET CASH FLOWS OF THE PERIODS
Projects 
Initial outlays 
1^{st} year Q_{1} 
2^{nd} year Q_{2} 
3^{rd} year Q_{3} 
4^{th} year Q_{4} 
5^{th} year Q_{5} 
A 
800 
50 
150 
250 
350 
450 
B 
950 
100 
200 
300 
350 
500 
C 
750 
50 
100 
400 
300 
200 
The interest rate is 10%. Considering that the net cash flows are maintained uniform along the year.
Obtain the classification of the projects according to the criteria of Payback and NPV
PR_2.02_06. A firm has the possibility of investing in one of these three projects: OUTCOMES: NPV_{1} = 2,913.29; NPV_{2} = 627.36; NPV_{3} = 13,868.91; PB_{1} = x y, 9 m and 18 d; PB_{2} = x y, 8 m and 17 d; PB_{3} = x y, 7 m and 15 d SOL_PR_2.02_06


Net cash flows 

Projects 
Initial outlay 
1^{st} year 
2^{nd} year 
3^{rd} year 
P1 
180,000 
 
100,000 
100,000 
P2 
190,000 
70,000 
70,000 
70,000 
P3 
160,000 
110,000 
 
80,000 
a. Which one do you choose according to the criteria of Payback? Considering that the cash flows are obtained in an uniform way along the year.
b. Which one do you choose according to the criteria of net present value, NPV, if the interest rate is 5%?
PR_2.03_06. A project of investment presents the following data: initial outlay of 1,500 m.u.; annual interest rate 6% and: OUTCOMES: NPV = 239.51; PB = x y, 9 m and 18 d SOL_PR_2.03_06
YEARS 
COLLECTIONS 
PAYMENTS 
1 
600 
300 
2 
700 
400 
3 
1,000 
500 
4 
1,000 
500 
5 
1,000 
500 
Calculate the NPV and the Payback of the project
PR_2.04_06. Given the following projects of investment: OUTCOMES: NPV_{1} = 312.6; NPV_{2} = 98.8; PB_{1} = x y and 8 m; PB_{2} = x y and 10 m SOL_PR_2.04_06

PROJECT 1 
PROJECT 2 

INITIAL OUTLAY 
5,000 
5,000 

NET CASH FLOWS 
1^{st} year 
 
1,000 
2^{nd} year 
3,000 
 

3^{rd} year 
3,000 
4,800 
Calculate: If we suposse that the net cash flows are obtained in an uniform way along the year.
Which project of investment is preferable according to the Payback?
Given an annual interest rate of 5%. Which project would you choose according to the NPV or net present value?
PR_2.05_06. The firm “Ciclomasa” dedicates itself to the sale of sport machines and it's thinking about the possibility of expand its business towards the sale of clothes and complements used to the sport. In order to that, it has planned an initial outlay of 600,000€ and the following net cash flows: OUTCOMES: NPV = 246,663.3; PB = x y, 7 m and 11 d SOL_PR_2.05_06
YEARS 
NET CASH FLOWS 
1 
200,000 
2 
240,000 
3 
260,000 
4 
260,000 
Determine if it is interesting to make the investment according to the Payback and according to the Net Present Value, given an interest rate of 5%. Explain the economic meaning.
PR_2.06_06. Order the following projects of investment (from best to worst) according to the criteria of Net Present Value, being the annual interest rate 7% and indicating whin ones are viable. OUTCOMES: NPV_{X} = 47,546.43; NPV_{Y} = 41,673.84; NPV_{Z} = 43,018.64 SOL_PR_2.06_06
Projects of investment 
A 
Q_{1} 
Q_{2} 
Q_{3} 
Q_{4} 
X 
22,000 
8,500 
17,000 
25,500 
34,000 
Y 
31,000 
7,300 
17,300 
27,300 
37,300 
Z 
31,500 
22,000 
22,000 
22,000 
22,000 
PR_2.01_07. The firm Valpe, Ltd. has three projects of investment, that mean an outlay and ones net cash flows that appear in the following table: OUTCOMES: NPV_{X} = 36,724.12; NPV_{Y} = 24,474.1; NPV_{Z} = 12,962.03; PB_{X} = x y, 4 m and 9 d; PB_{Y} = x y and 6 m; PB_{Z} = x y, 8 m and 19 d SOL_PR_2.01_07
Projects of investment 
Initial outlay 
INPUTS 

1^{st} year 
2^{nd} year 
3^{rd} year 
4^{th} year 

X 
20,000 
15,000 
14,000 
20,000 
12,000 
Y 
23,500 
14,000 
19,000 
18,000 
 
Z 
14,000 
13,000 
 10,500 
16,000 
10,800 
Calculate the more profitable investment, if the interest rate is 3%, according to the methods of Net Present Value and the Payback of each one of them
PR_2.02_07. A project of investment had an initial outlay of 200,000€ and the cash flows of the first and the second year were, 80,000€ and 60,000€ respectively. Calculate the cash flow of the third year knowing that the Payback of the investment was two years and nine months. OUTCOME: X = 80,000€ SOL_PR_2.02_07
PR_2.03_07. The firm “GOLDFINCH, Ltd”, is planning to make a new investment and it has several options: option A and option B. In the following table appear all the data related to the investment in euros. The initial outlay of both investments is 90,000€ and the interest rate is 5%. OUTCOMES: NPV_{A} = 26,682.87; NPV_{B} = 29,771.08; PB_{A} = x y and 4 m; PB_{B} = x y, 7 m and 6 d SOL_PR_2.03_07

OPTION A 
OPTION B 


COLLECTIONS 
PAYMENTS 
COLLECTIONS 
PAYMENTS 
1^{st} year 
80,000 
50,000 
180,000 
120,000 
2^{nd} year 
140,000 
100,000 
180,000 
130,000 
3^{rd} year 
150,000 
90,000 
180,000 
160,000 
Use the criteria of Net Present Value and Payback.
Which option is the best according to each one of the criteria and why
PR_2.04_07. The firm of cans of vegetable Vegetalinea, Ltd., wants to expand its installed capacity to the canning of its products. In order to that it has selected three alternatives. The expected cash flows in the next four years for each one of the projects of investment are the following: OUTCOMES: NPV_{1} = 4,169.74; NPV_{2} = 2,119.51; NPV_{3} = 2,226.21; PB_{1} = x y and 2 m; PB_{2} = x y, 1 m and 10 d; PB_{3} = x y, 5 m and 20 d SOL_PR_2.04_07

1^{st} year 
2^{nd} year 
3^{rd} year 
4^{th} year 
1^{st} alternative 
500 
2,000 
3,000 
3,200 
2^{nd} alternative 
1,000 
2,300 
3,200 
4,500 
3^{rd} alternative 
2,000 
500 
4,000 
5,000 
The needed investments are 2,000, 5,000 and 7,000 monetary unities, respectively, for the 1^{st}, 2^{nd} and 3^{rd} alternatives. The planned interest rate is 7%.
Determine the best alternative for the firm by using the following methods:
The Payback
The Net Present Value.
PR_2.01_08. The firm plans to make a new investment. In order to that it has the two following possibilities: OUTCOMES: NPV_{A} = 3,971.87; NPV_{B} = 1,456.21 SOL_PR_2.01_08
Year 
Project A 
Project B 



Collections 
Payments 
Collections 
Payments 
0 
0 
3,000 
0 
2,000 
1 
2,000 
1,000 
3,000 
4,000 
2 
5,000 
2,000 
5,000 
1,000 
3 
6,000 
2,000 
3,000 
2,000 
Calculate the cash flows of each period
Select the preferable investment, according to the criteria of NPV, if the interest rate is 6%
PR_2.02_08. The data related to two projects of investment that a firm wants to evaluate are in the attached table: OUTCOMES: NPV_{A} = 5,768.35; NPV_{B} = 3,558.56; PB_{A} = x y and 8 m; PB_{B} = x y, 10 m and 15 d SOL_PR_2.02_08
Project 
Initial outlay 
Cash flow 1^{st} year 
Cash flow 2^{nd} year 
Cash flow 3^{rd} year 
Cash flow 4^{th} year 
Cash flow 5^{th} year 

A 
10,000 
0 
0 
6,000 
6,000 
8,000 
B 
16,000 
4,000 
5,000 
8,000 
3,000 
3,000 
If the annual interest rate is 6%.
Put in order the investments according to the criteria of Net Present Value (NPV)
Put in order the investments according to the criteria of Payback. Consider that the cash flows are obtained in an uniform way along the year.
Comment the outcomes
PR_2.03_08. A firm is studying two projects of investment: Italica and Betica. The project Italica means an initial outlay of 120,000€ and it's expected to obtain, in each one of the five years, a net cash flow of 36,000€. The project Betica also means an initial outlay of 120,000€, but the net cash flows expected during the five years of life of the project are: 18,000€ 1^{st} year, 30,000€ 2^{nd} year, 54,000€ 3^{rd} year, 48,000€ 4^{th} year and 43,000€ 5^{th} year. Being the interest rate 6%, determine which of the two investments is the best according to the NPV method. OUTCOMES: NPV_{I} = 31,645.08; NPV_{B} = 39,173.06 SOL_PR_2.03_08
PR_2.04_08. The firm X produces and sells chocolates. As the business works very well in Spain and it has available money, it's thinking about to expand to Poland, building there a new factory. The investment lasts 4 years, being the net cash flow of the 1^{st} year 120,000€, 132,000€ 2^{nd} year, 145,000€ 3^{rd} year and 160,000 4^{th} year. The initial outlay is 290,000€ and the interest rate is 6% OUTCOMES: NPV = 189,166.87; PB = x y, 3 m and 4 d SOL_PR_2.04_08
Calculate:
The Net Present Value of the investment
The Payback. Consider that the cash flow are obtained in an uniform way along the year
Explain the economic meaning of the obtained outcomes
PR_2.05_08. A businessman is thinking about to make an investment to expand his facilities, in order to that he must pay 15,000€ in the initial moment. The collections are 8,100€ 1^{st} year and 12,000€ the following years. The payments are 4,500€ 1^{st} year and 5,400€ the rest of the years. If the useful life is 6 years and the annual interest rate is 6%, obtain the NPV of the investment and the Payback OUTCOMES: NPV = 14,624.16; PB = x y, 8 m and 22 d SOL_PR_2.05_08
PR_2.06_08. A firm is thinking about the two following possible projects of investment: OUTCOMES: NPV_{A} = 2,870.02; NPV_{B} = 3,073.63 SOL_PR_2.06_08

Initial outlay 
Cash flow 1^{st} year 
Cash flow 2^{nd} year 
Cash flow 3^{rd} year 

Project A 
10,000 
3,000 
5,000 
8,000 
Project B 
9,000 
7,000 
6,000 
1,000 
Determine which is the best option according to the net present value. The interest rate is 10%. Explain the economic meaning of the obtained outcomes
PR_2.01_09. We have a project of investment with the follwing data:
R_{0} = 80 m.u. F_{1} = 70 m.u. F_{2} = 30 m.u. F_{3} = 30 m.u.
The interest rate is 30%; we want to know:
The net present value
Is it acceptable the investment?
OUTCOME: NPV = 5.25 SOL_PR_2.01_09
PR_2.02_09. A firm is thinking about the following two projects of investment: RESULTADOS : VAN_{A} = 96,34; VAN_{B} = 110,53 SOL_PR_2.02_09
Project 
Initial outlay 
Cash flow 1^{st} year 
Cash flow 2^{nd} year 
Cash flow 3^{rd} year 
Cash flow 4^{th} year 

A 
500 
100 
0 
400 
300 
B 
600 
300 
100 
200 
300 
Determine the net present value of each one of the projects of investment. The interest rate is 10%
Which is the best option and why?
PR_2.03_09. The firm “2^{nd} year of high school degree, Ltd” sells chemical products and it's thinking to expand its business to the sale of plant health products to the agriculture. In order to that it has the possibility of make the following two projects : OUTCOMES: PB_{1} = x y, PB_{2} = x y; NPV_{1} = 2,446.22; NPV_{2} = 862.65 SOL_PR_2.03_09

1^{st} year 
2^{nd} year 
3^{rd} year 



Collections 
Payments 
Collections 
Payments 
Collections 
Payments 
Project 1 
600€ 
750€ 
2,200€ 
350€ 
3,800€ 
400€ 
Project 2 
4,000€ 
3,000€ 
5,000€ 
4,000€ 
6,000€ 
5,900€ 
Determine the more profitable project knowing that the project 1 has an initial outlay of 1,700 and the project 2 another of 1,000€
According to the criteria of Payback
According to the net present value. The interest rate is 8%
PR_2.04_09. Given the two projects of investment which initial outlays and cash flows are in the following table: OUTCOMES: PB_{A} = x y; PB_{B} = x y; NPV_{A} =  323.87; NPV_{B} = 8,628.84 SOL_PR_2.04_09

Cash flows (m.u.) 



Projects 
1^{st} year 
2^{nd} year 
3^{rd} year 
4^{th} year 
Initial outlays 
A 
400 
3,600 
100 
100 
4,000 
B 
800 
2,000 
1,200 
12,000 
4,000 
Which is the best investment according to the Payback?
Which is the net present value of each one of the projects. The interest rate is 7%
PR_2.05_09. A catering industry firm, wants to make an investment and needs to value the best according to the criteria of the net present value. The interest rate is 4%. Which is the best options? (Quantities in euros) OUTCOMES : NPV_{A} = 1,715.6; NPV_{B} =  253.3; NPV_{C} = 2,011.13; PB_{A} = x y and 6 m; PB_{B} = x y and 7m; PB_{C} = x y and 9 m SOL_PR_2.05_09
Investment 
Initial outlay 
F1 
F2 
F3 

A 
1,600 
1,000 
1,200 
1,400 
B 
2,000 
500 
600 
800 
C 
2,400 
1,200 
1,600 
2,000 
Which would be the best option if the used method is the Payback?
SOLUTIONS TO THE PROBLEMS OF 3^{rd} PART TOPIC 9.
NPV_{X} = 18,000 + 7,000 : 1.07 + 9,000 : 1.07^{2} + 8,000 : 1.07^{3} + 12,000 : 1.07^{4}
NPV_{X} = 18,000 + 6,542.06 + 7,860.95 + 6,530.38 + 9,154.74 = 12,088.13€
NPV_{Y} = 30,000 + 15,000 : 1.07 + 15,000 : 1.07^{2} + 15,000 : 1.07^{3}
NPV_{Y} = 30,000 + 14,018.69 + 13,101.58 + 12,244.47 = 9,364.74€
NPV_{Z} = 25,000 + 12,000 : 1.07 + 11,000 : 1.07^{2} + 10,000 : 1.07^{3}
NPVZ = 25,000 + 11,214.95 + 9,607.83 + 8,162.98 = 3,985.75€
According to this method the best investment is the investment X because it obtains more profit than the others
NPV =  600,000 + 50,000 : 1.08 + 140,000 : 1.08^{2} + 235,000 : 1.08^{3} + 235,000 : 1.08^{4}
NPV =  600,000 + 46,296.296 + 120,027.434 + 186,550.576 + 172,732.015 = 74,393.679€
According to this method this investment wouldn't be interesting to the firm because it's lossing money
The Payback is more than 3 years. We are going to calculate the months:
235,000  12 months
175,000  x months
x = (175,000 x 12) : 235,000 = 8.94 months. We are going to calculate the dates:
1 month  30 days
0.94 monts  x days
x= 0.94 x 30 = 28 days. The payback is 3 years, 8 months and 28 days
According to this method this investment would be interesting to the firm because it recovers the initial outlay before the planned five years
Raw material rotation = 977,000,000 : 63,000,000 = 15.51
Raw material conversion period = 365 : 15.51 = 23.53 days
Good in process rotation = 2,104,000,000 : 48,000,000 = 43.83
Good in process conversion period = 365 : 43.83 = 8.33 days
Finished goods rotation = 2,012,000,000 : 115,000,000 = 17.50
Finished goods conversion period = 365 : 17.50 = 20.86 days
Payment from customers rotation = 2,415,000,000 : 138,000,000 = 17.5
Receivables conversion period = 365 : 17.5 = 20.86
Cash conversion cycle = 23.53 + 8.33 + 20.86 + 20.86 = 73.58
This firm takes 74 days to realize the full operating cycle; being this the period of time that the firm takes to recover the investments in current assets that it needs to do the aforementioned cycle
NPV_{A} =  1,000,000 + 100,000 : 1.07 + 150,000 : 1.07^{2} + 200,000 : 1.07^{3} + 250,000 : 1.07^{4} + 300,000 : 1,07^{5} =  207,647€
NPV_{B} =  1,500,000 + 200,000 : 1.07 + 300,000 : 1.07^{2} + 350,000 : 1.07^{3} + 400,000 : 1.07^{4} + 500,000 : 1.07^{5} =  103,697€
NPV_{C} =  1,700,000 + 400,000 : 1.07 + 600,000 : 1.07^{2} + 300,000 : 1.07^{3} + 600,000 : 1.07^{4} + 400,000 : 1.07^{5} = 185.716€
The best investment is project C because it's the only one with a positive NPV
a)
a.1)
NPV_{A} =  10,000,000 + 6,000,000 : 1.06^{3} + 6,000,000 : 1.06^{4} + 8,000,000 : 1.06^{5} = 5,768,343.06
NPV_{B} =  20,000,000 + 3,000,000 : 1.06 + 4,000,000 : 1.06^{2} + 5,000,000 : 1.06^{3} + 6,000,000 : 1.06^{4} + 8,000,000 : 1.06^{5} = 1,318,898.21
NPV_{C} = 16,000,000 + 4,000,000 : 1.06 + 5,000,000 : 1.06^{2} + 8,000,000 : 1.06^{3} + 3,000,000 : 1.06^{4} + 3,000,000 : 1.06^{5} = 3,558,576.88
According to this criteria the best project would be project A, the second best project would be project C and the last one would be project B
a.2)
The Payback of project A will be more than 3 years. We are going to calculate the months:
6,000,000  12 months
4,000,000  x months
x = (4,000,000 x 12) : 6,000,000 = 8 months
The Payback of project A will be 3 years and 8 months
The Payback of project B will be more than 4 years. We are going to calculate the months:
8,000,000  12 months
2,000,000  x months
x = (2,000,000 x 12) : 8,000,000 = 3 months
The Payback of project B will be 4 years and 3 months
The Payback of project C will be more than 2 years. We are going to calculate the months
8,000,000  12 months
7,000,000  x monts
x = (7,000,000 x 12) : 8,000,000 = 10.5 months. We are going to calculate the days
1 month  30 days
0,5 months  x days
x = 0.5 x 30 = 15 days
The Payback of project C will be 2 years, 10 months and 15 days
According to this criteria the best project would be project C, the second best project would be project A and the last one would be project B
b) The NPV shows us the quantity that we earned if we would move all the collections and the payments to the current moment; the hight profit the best investment
The Payback calculates the period of time to recover the initial outlay; the least time the best investment
NPV_{A} = 10,000,000 + 1,000,000 : 1.08 – 2,000,000 : 1.08^{2} + 6,000,000 : 1.08^{3} + 6,000,000 : 1.08^{4} + 8,000,000 : 1.08^{5} = 3,829,086.43
NPV_{B} = 18,000,000 – 3,000,000 : 1.08 + 4,000,000 : 1.08^{2} + 5,000,000 : 1.08^{3} + 6,000,000 : 1.08^{4} + 8,000,000 : 1.08^{5} = 3,524,416.59
NPV_{C} = 16,000,000 + 4,000,000 : 1.08 + 5,000,000 : 1.08^{2} + 8,000,000 : 1.08^{3} + 3,000,000 : 1.08^{4} + 3,000,000 : 1.08^{5} = 2,587,894.88
According to this criteria the best project would be project A, the second best project would be project C and the last one would be project B
The Payback of A is more than 3 years. We are going to calculate the months
6,000,000  12 months
5,000,000  x months
x = (5,000,000 x 12) : 6,000,000 = 10 months
The Payback is 3 years and 10 months
The Payback of B is more than 4 years. We are going to calculate the months
8,000,000  12 months
6,000,000  x months
x = 9 months
The Payback of B is 4 years and 9 months
The Payback of C is more than 2 years. We are going to calculate the months
8,000,000  12 months
7,000,000  x months
x = 10.5 months. We are going to calculate the days
1 month  30 days
0.5months  x days
x = 0.5 x 30 = 15 days
The Payback of C is 2 years, 10 months and 15 days
According to the Payback the best project is project C, the second best project is project A and the last one es project B
PB_{A} = 2 years
PB_{B} = 3 years
Therefore, the best investment, according to the Payback is the investment A
NPV_{A} = 10,000 + 5,000 : 1.1 + 5,000 : 1.1^{2} + 5,000 : 1.1^{3} + 5,000 : 1.1^{4} = 5,849.50
NPV_{B} = 10,000 + 2,000 : 1.1 + 4,000 : 1.1^{2} + 4,000 : 1.1^{3} + 20,000 : 1.1^{4} = 11,789.50
Therefore, the best investment according to the NPV is the investment B because it has the highest NPV
There isn't an agreement between both criteria because according to the Payback teh best investment is investment A and according to the NPV, the best investment is investment B
The NPV shows us the quantity that we earned if we would move all the collections and the payments to the current moment; the hight profit the best investment
The Payback calculates the period of time to recover the initial outlay; the least time the best investment
NPV_{A} = 10,000 + 2,000 : 1.1 + 6,000 : 1.1^{2} + 8,000 : 1.1^{3} = 2,787.37
NPV_{B} =  8,000 + 3,000 : 1.1 + 5,000 : 1.1^{2} + 3,000 : 1.1^{3} = 1,113.44
According to this criteria the best investment is investment A because it has a higher NPV
The Payback of A is more than 2 years. We are going to calculate the months
8,000  12 months
2,000  x months x = 3 months
The Payback of A is 2 years and 3 months
The Payback of B is 2 years
According to this criteria the best investment is investment B because we recover the initial outlay before than in the other investment
There isn't an agreement between both criteria because according to the Payback the best investment is B and according to the NPV the best investment is A
The NPV shows us the quantity that we earned if we would move all the collections and the payments to the current moment; the hight profit the best investment
The Payback calculates the period of time to recover the initial outlay; the least time the best investment
Nominal value = 73,647 : 4,900 = 15.03 €/share
Market value = 15.03 x 1.65 = 24.80 €/share
Theoretical value = 2.40/0.07 = 34.29 €/share
NPV_{D} =  90,000 – 10,000 : 1.07 + 40,000 : 1.07^{2} + 60,000 : 1.07^{3} = 15,430.37€
NPV_{E} =  78,000 + 60,000 : 1.07 + 60,000 : 1,07^{2} + 60,000 : 1,07^{3} = 79,458.96€
According to this criteria, the expansion is the best option
The Payback of the diversification is 3 years
The Payback of the expansion is more than 1 year. We are going to calculate the months
60,000  12 months
18,000  x months x = 3.6 months. We are going to calculate the days
1 month  30 days
0.6 months  x days x = 18 days
The Payback of the expansion is 1 year, 3 months and 18 days
According to this criteria, the firm would opt for the expansion, as well
x  12 months
30,000  9 months x = 40,000€
Nominal value = 120,000 : 300 = 400€
Theoretical value = (120,000 + 24,000) : 300 = 480€
Distributing dividend per share = 12,000 : 300 = 40€
Net worth = 120,000 + 24,000 = 144,000€
NPV = 1,500 + 300 : 1.05 + 300 : 1.05^{2} + 500 : 1.05^{3} + 500 : 1.05^{4} + 500 : 1.05^{5} = 292.85 m.u.
NPV_{A} = 25,000 + 30,000 : 1.065^{3} + 12,000 : 1.065^{4} = 9,163.35€
NPV_{B} = 20,000 – 5,000 : 1.065 – 2,000 : 1.065^{2} + 15,000 : 1.065^{3} + 15,000 : 1.065^{4} = 2,380.57€
NPV_{C} = 16,000 + 5,000 : 1.065 + 6,000 : 1.065^{2} + 7,000 : 1065^{3} + 8,000 : 1.065^{4} = 5,998.32€
According to this criteria the best project is project A, the second best project is project C and the last one is project B
The Payback of A is more than 2 years. We are going to calculate the months
30,000  12 months
25,000  x months x = 10 months
The Paybak of A es 2 years and 10 months
The Payback of B is more than 3 years. We are going to calculate the months
15,000  12 months
12,000  x months x = 9.6 months. We are going to calculate the days
1 month  30 days
0.6 months  x days x = 18 days
The Payback of B is 3 years, 9 months and 18 days
The Payback of C is more than 2 years. We are going to calculate the months
7,000  12 months
5,000  x months x = 8.57 months. We are going to calculate the days
1 month  30 days
0.57 months  x days x = 17 days
The Payback of C is 2 years, 8 months and 17 days
According to this criteria the best is C, the second is A and the last one is B
NPV_{A} = 1,000,000 + 300,000 : 1.05 + 300,000 : 1.05^{2} + 300,000 : 1.05^{3} + 300,000 : 1.05^{4} + 300,000 : 1.05^{5} = 298,843€
NPV_{B} = 1,000,000 + 150,000 : 1.05 + 250,000 : 1.05^{2} + 450,000 : 1.05^{3} + 400,000 : 1.05^{4} + 350,000 : 1.05^{5} = 361,656.58€
According to this criteria, project B is the best option because the NPV is the highest
REPETIDO
Igual que 2.12_03
NPV_{A} = 10,000 + 2,000 : 1.08 + 2,500 : 1.08^{2} + 3,000 : 1.08^{3} + 3,000 : 1.08^{4} + 3,100 : 1.08^{5} = 691.6€
NPV_{B} = 14,100 + 3,000 : 1.08 + 3,400 : 1.08^{2} + 3,200 : 1.08^{3} + 3,000 : 1.08^{4} + 3,000 : 1.08^{5} = 1,620.17€
According to the NPV method, project a is preferable to project B
The Payback of project A is more than 3 years. We are going to calculate the months
3,000  12 months
2,500  x months x = 10 months
The Payback of project A is 3 years and 10 months
The Payback of project B is more than 4 years. We are going to calculate the months
3,000  12 months
1,500  x months x = 6 months
The Payback of project B is 4 years and 6 months.
According to this criteria, project A is preferable to project B
Share Capital = 50,000 x 1,000 = 50,000,000 m.u.
The shares quote above par
Theoretical value of each share = (50,000,000 + 10,000,000) : 50,000 = 1,200 m.u.
600       12
500       x x = 10 m Payback of investment 1 = 1 year and 10 months
10,000         12
400            x x = 0.48
1 month          30 days
0.48 months       x days x = 14 days Payback of investment 2 = 2 years and 14 days
According to the Payback, investment 1 is preferable to investment 2
Investment 2 is more profitable because, although we take more time, we get far more money
Cash flows year 0 (before taxes) =  13,000
Cash flows 1^{st} year (before taxes) = 6,000 – 1,050
Cash flows 2^{nd} year (before taxes) = 12,000 – 1,130
Cash flows 3^{rd} year (before taxes) = 12,500 – 1,350
Cash flows 4^{th} year (before taxes) = 20,000 – 1,350
Taxes 1^{st} year = (6,000 – 1,050) x 0.25 = 1,237.5
Taxes 2^{nd} year = (12,000 – 1,130) x 0.25 = 2,717.5
Taxes 3^{rd} year = (12,500 – 1,350) x 0.25 = 2,787.5
Taxes 4^{th} year = (20,000 – 1,350) x 0.25 = 4,662.5
Cash flows year 0 (after taxes) =  13,000
Cash flows 1^{st} year (after taxes) = 6,000 – 1,050 – 1,237.5 = 3,712.5
Cash flows 2^{nd} year (after taxes) = 12,000 – 1,130 – 2,717,5 = 8,152.5
Cash flows 3^{rd} year (after taxes) = 12,500 – 1,350 – 2,787.5 = 8,362.5
Cash flows 4^{th} year (after taxes) = 20,000 – 1,350 – 4,662.5 = 13,987.5
NPV =  13,000 + (3,712.5 : 1.15) + (8,152.5 : 1.15^{2}) + (8,362.5 : 1.15^{3}) + (13,987.5 : 1.15^{4}) = 9,888.6 The investment is a good idea for the firm
NPV =  3,000 + (1,000 : 1.05) + (1,000 : 1.05^{2}) + (1,000 : 1.05^{3}) + (1,200 : 1.05^{4}) = 710.49€
NPV_{X} =  11,000 + (8,000 : 1.04) + (10,000 : 1.04^{2})+ (12,000 : 1.04^{3}) =
NPV_{X} =  11,000 + 7,692.31 + 9,245.56 + 10,667.96 = 16,605.83
NPV_{Y} =  11,000 + (10,000 : 1.04) + (10,000 : 1.04^{2}) + (10,000 : 1.04^{3}) =
NPV_{Y} =  11,000 + 9,615.38 + 9,245.56 + 8,889.96 = 16,750.9
The investment X is more interesting than investment Y because X has the highest NPV
NPV_{A} =  10,000 + (7,500 : 1.08) + (3,600 : 1.08^{2}) + (500 : 1.08^{3}) =
NPV_{A} =  10,000 + 6,944.44 + 3,086.42 + 396.92 = 427.78
NPV_{B} =  10,000 + (4,000 : 1.08) + (4,000 : 1.08^{2}) + (4.000 : 1.08^{3}) =
NPV_{B} =  10,000 + 3,703.70 + 3,429.36 + 3,175.33 = 308.39
NPV_{C} =  10,000 + (8,000 : 1.08^{2}) + (3,000 : 1.08^{3}) =
NPV_{C} =  10,000 + 6,858.71 + 2,381.50 =  759.79
According to this criteria, the best project is project A because it has the highest NPV
X = (2,500 x 12) : 3,600 = 8.33 m. __________ X = 0.33 x 30 = 9.9 d. ____ PB_{A} = 1 y, 8 m and 10 d.
X = (2,000 x 12) : 4,000 = 6 m. _______ PB_{B} = 2 y and 6 m.
X = (2,000 x 12) : 3,000 = 8 m. ________ PB_{C} = 2 y and 8 m.
According to this criteria, the best project is project A because it has the least Payback
X = (30,000 x 12) : 45,000 = 8 m. _______ PB_{1} = 2 y and 8 m
X = (38,000 x 12) : 52,000 = 8.77 m. ______ X = 0.77 x 30 = 23.1 d. _____ PB_{2} = 2 y, 8 m and 23 d
X = (40,000 x 12) : 55,000 = 8.73 m. ______ X = 0.73 x 30 = 21.9 d. _____ PB_{3} = 2 y, 8 m and 22 d
According to this criteria, the best option is project 1
NPV_{1} =  80,000 + (50,000 : 1.045^{2}) + (45,000 : 1.045^{3})
NPV_{1} =  80,000 + 45,786.50 + 39,433.35 = 5,219.85
NPV_{2} =  90,000 + (52,000 : 1.045) + (52,000 : 1.045^{3})
NPV_{2} =  90,000 + 49,760.77 + 45,567.42 = 5,328.19
NPV_{3} =  80,000 + (40,000 : 1.045) + (55,000 : 1.045^{3})
NPV_{3} =  80,000 + 38,277.51 + 48,196.31 = 6,473.82
According to this criteria, the best option is project 3
X = (5,000 x 12) : 8,000 = 7.5 m ____ X = 0.5 x 30 = 15 d _____ PB_{A} = 2 y, 7m and 15 d
X = (19,000 x 12) : 20,000 = 11.4 m _____ X = 0.4 x 30 = 12 d _______ PB_{B} = 3 y, 11 m and 12 d
X = (13,000 x 12) : 14,000 = 11.14 m ______ X = 0.14 x 30 = 4.2 d _____ PB_{C} = 2 y, 11 m. and 4 d
According to the Payback the best option is investment A because it has the least Payback. I agree with the chief financial officer because investment A is the option that is recovered before and it's the option that more money recovers
NPV_{A} =  20,000 + (10,000 : 1.04) + (8,000 : 1.04^{2}) + (20,000 : 1.04^{3}) + (4,000 : 1.04^{4})
NPV_{A} =  20,000 + 9,615.38 + 7,396.45 + 17,779.93 + 3,419.22 = 18,210.98
NPV_{B} =  27,000 + (8.000 : 1.04) + (18,000 : 1.04^{2})+ (16,000 : 1.04^{3})
NPV_{B} =  27,000 + 7,692.31 + 16,642.01 + 14,223.94 = 11,558.26
NPV_{C} =  8,000 + (6,000 : 1.04) – (1,000 : 1.04^{2}) + (12,000 : 1.04^{3}) + (1,600 : 1.04^{4})
NPV_{C} =  8,000 + 5,769.23 – 924.23 + 10,667.96 + 1,367.69 = 8,880.32
According to this criteria the order would be: A – B  C
X = (2,000 x 12) : 20,000 = 1.2 m _____ X = 0.2 x 30 = 6 d ____ PB_{A} = 2 y, 1 m and 6 d
X = (1,000 x 12) : 16,000 = 0.75 m _____ X = 0.75 x 30 = 22.5 d ___ PB_{B} = 2 y and 23 d
X = (3,000 x 12) : 12,000 = 3 m ______ PB_{C} = 2 y and 3 m
According to this criteria the order would be: B – A  C
X = (4,000 x 12) : 5,000 = 9.6 m _____ X = 0.6 x 30 = 18 d ____ PB_{A} = 1 y, 9 m. and 18 d
x = (5,000 x 12) : 20,000 = 3 m ______ PB_{B} = 2 y and 3 m
According to this criteria the best option is investment A because we recover it before than investment B
NPV_{A} =  10,000 + (6,000 : 1.06) + (5,000 : 1.06^{2}) + (100 : 1.06^{3})
NPV_{A} =  10,000 + 5,660.38 + 4,449.98 + 83.96 = 194.32
NPV_{B} =  10,000 + (1,000 : 1.06) + (4.000 : 1.06^{2}) + (20.000 : 1.06^{3})
NPV_{B} =  10,000 + 943.40 + 3,559.99 + 16,792.39 = 11,295.78
According to this criteria the best option is investment B
The two methods don't coincide to indicate which investment is the best because the Payback looks for which investment is recovered before and the NPV looks for which investment is going to reach a highest profit. The best criteria is the NPV.
NPV_{A} =  800 – (50 : 1.1) + (150 : 1.1^{2}) + (250 : 1.1^{3}) + (350 : 1.1^{4}) + (450 : 1.1^{5})
NPV_{A} =  800 – 45.45 + 123.97 + 187.83 + 239.05 + 279.41 =  15.19
NPV_{B} =  950 + (100 : 1.1) + (200 : 1.1^{2}) + (300 : 1.1^{3}) + (350 : 1.1^{4}) + (500 : 1.1^{5})
NPV_{B} =  950 + 90.91 + 165.29 + 225.39 + 239.05 + 310.46 = 81.1
NPV_{C} =  750 – (50 : 1.1) + (100 : 1.1^{2}) + (400 : 1.1^{3}) + (300 : 1.1^{4}) + (200 : 1.1^{5})
NPV_{C} =  750 – 45.45 + 82.64 + 300.53 + 204.90 + 124.18 =  83.2
According to this criteria the only one interesting option is investment B, because the others are negative; the order would be: B – A  C
X = (100 x 12) : 450 = 2.67 months
X = (0.67 x 30) : 1 = 20.1 days
PB_{A} = 4 y, 2 m and 20 d
PB_{B} = 4 years
PB_{C} = 4 years
According to this criteria, investments B and C would be in the first place and investment A in the last place
NPV_{1} =  180,000 + (100,000 : 1.05^{2}) + (100,000 : 1.05^{3}) =  180,000 + 90,702.95 + 86,383.76
NPV_{1} =  2,913.29
NPV_{2} =  190,000 + (70,000 : 1.05) + (70,000 : 1.05^{2}) + (70,000 : 1.05^{3})
NPV_{2} =  190,000 + 66,666.67 + 63,492.06 + 60,468.63 = 627.36
NPV_{3} =  160,000 + (110,000 : 1.05) + (80,000 : 1.05^{3}) =  160,000 + 104,761.90 + 69,107.01
NPV_{3} = 13,868.91
According to this criteria the best option is investment 3 because it has the highest NPV
X = (80,000 x 12) : 100,000 = 9.6 months
X = (0.6 x 30) : 1 = 18 days
PB_{1} = 2 years, 9 months and 18 days
X = (50,000 x 12) : 70,000 = 8.57 months
X = (0.57 x 30) : 1 = 17.1 days
PB_{2} = 2 years, 8 months and 17 days
X = (50,000 x 12) : 80,000 = 7.5 months
X = (0.5 x 30) : 1 = 15 days
PB_{3} = 2 years, 7 months and 15 days
According to this criteria the best option is investment 3 because it is recovered before than the others
NPV =  1,500 + (300 : 1.06) + (300 : 1.06^{2}) + (500 : 1.06^{3}) + (500 : 1.06^{4}) + (500 : 1.06^{5})
NPV =  1,500 + 283.02 + 267.00 + 419.81 + 396.05 + 373.63 = 239.51
X = (400 x 12) : 500 = 9.6 months
X = (0.6 x 30) : 1 = 18 days
PB = 3 years, 9 months and 18 days
NPV_{1} =  5,000 + (3,000 : 1.05^{2}) + (3,000 : 1.05^{3}) =  5,000 + 2,721.09 + 2,591.51 = 312.6
NPV_{2} =  5,000 + (1,000 : 1.05) + (4,800 : 1.05^{3}) =  5,000 + 952.38 + 4,146.42 = 98.8
According to this criteria the best option would be investment 1 because it has the highest NPV
X = (2,000 x 12) : 3,000 = 8 months
PB_{1} = 2 years and 8 months
X = (4,000 x 12) : 4,800 = 10 months
PB_{2} = 2 years and 10 months
Accordign to this criteria the best option would be project a because it has the least Payback
NPV =  600,000 + (200,000 : 1.05) + (240,000 : 1.05^{2}) + (260,000 : 1.05^{3}) + (260,000 : 1.05^{4})
NPV =  600,000 + 190,476.19 + 217,687.07 + 224,597.78 + 213,902.26 = 246,663.3
According to this criteria would be interesting to make the investment because it has a positive NPV
X = (160.000 x 12) : 260.000 = 7,38 months
X = (0,38 x 30) : 1 = 11,4 days
PB = 2 years, 7 months y 11 days
Según este criterio no podemos decir si interesa o no realizarla ya que no se nos ha dado un plazo máximo de recuperación
NPV_{X} =  22,000 + (8,500 : 1.07) + (17,000 : 1.07^{2}) + (25,500 : 1.07^{3}) + (34,000 : 1.07^{4})
NPV_{X} =  22,000 + 7,943.93 + 14,848.46 + 20,815.60 + 25,938.44 = 47,546.43
NPV_{Y} =  31,000 + (7,300 : 1.07) + (17,300 : 1.07^{2}) + (27,300 : 1.07^{3}) + (37,300 : 1.07^{4})
NPV_{Y} =  31,000 + 6,822.43 + 15,110.49 + 22,284.93 + 28,455.99 = 41,673.84
NPV_{Z} =  31,500 + (22,000 : 1.07) + (22,000 : 1.07^{2}) + (22,000 : 1.07^{3}) + (22,000 : 1.07^{4})
NPV_{Z} =  31,500 + 20,560.75 + 19,215.65 + 17,958.55 + 16,783.69 = 43,018.64
According to this criteria, from best to worts, the order would be: X – Z – Y. All the projects are viable because all of then are positive
NPV_{X} =  20,000 + (15,000 : 1.03) + (14,000 : 1.03^{2} )+ (20,000 : 1.03^{3} )+ (12,000 : 1.03^{4}) = 36,724.12
NPV_{Y} =  23,500 + (14,000 : 1.03) + (19,000 : 1.03^{2}) + (18,000 : 1.03^{3}) = 24,474.1
NPV_{Z} =  14,000 + (13,000 : 1.03) + (10,500 : 1.03^{2}) + (16,000 : 1.03^{3}) + (10,800 : 1.03^{4}) = 12,962.03
According to this criteria, the more profitable option is investment X because it has the highest NPV
PB_{X} = 1 y, 4 m and 9 d x = (5,000 x 12) : 14,000 = 4.29 m x= 0.29 x 30 = 8.7 = 9 d
PB_{Y} = 1 y and 6 m x = (9,500 x 12) : 19,000 = 6 m
PB_{Z} = 2 y, 8 m and 19 d x = (11,500 x 12) : 16,000 = 8.63 m x = 0.63 x 30 = 18.9 = 19 d
According to this criteria, the more profitable option is investment X because it recovers the initial outlay before than the others
R_{3} = (60,000 x 12) : 9 = 80,000€
NPV_{A} =  90,000 + (30,000 : 1.05) + (40,000 : 1.05^{2}) + (60,000 : 1.05^{3}) = 26,682.87€
NPV_{B} =  90,000 + (60,000 : 1.05) + (50,000 : 1.05^{2}) + (20,000 : 1.05^{3}) = 29,771.08€
According to this criteria, the best option is investment B because it has the highest NPV
PB_{A} = 2 y and 4 m
X = (20,000 x 12) : 60,000 = 4 m
PB_{B} = 1 y, 7 m and 6 d
X = (30,000 x 12) : 50,000 = 7.2 m x = 0.2 x 30 = 6 d
According to this criteria, the best option is investment B because it recovers the initial outlay before than the other
NPV_{1} =  2,000 – (500 : 1.07) + (2,000 : 1.07^{2}) + (3,000 : 1.07^{3}) + (3.200 : 1.07^{4}) = 4,169.74 m.u.
NPV_{2} =  5,000 – (1,000 : 1.07) + (2,300 : 1.07^{2}) + (3,200 : 1.07^{3}) + (4,500 : 1.07^{4}) = 2,119.51 m.u.
NPV_{3} =  7,000 – (2,000 : 1.07) – (500 : 1.07^{2}) + (4,000 : 1.07^{3}) + (5,000 : 1.07^{4}) =  2,226.21 m.u.
According to this criteria, the best option is investment 1 because it has the highest NPV
PB_{1} = 2 y and 2 m
X = (500 x 12) : 3,000 = 2 m
PB_{2} = 3 y, 1 m and 10 d
X = (500 x 12) : 4,500 = 1.33 m x = 0.33 x 30 = 9.9 d = 10 d
PB_{3} = It isn't recovered
According to this criteria, the best option is investment 1, because it has the least Payback
NPVa =  3,000 + (1,000 : 1.06) + (3,000 : 1.06^{2}) + (4,000 : 1.06^{3})
NPVa =  3,000 + 943.40 + 2,669.99 + 3,358.48 = 3,971.87
NPVb =  2,000 – (1,000 : 1.06) + (4,000 : 1.06^{2}) + (1,000 : 1.06^{3})
NPVb =  2,000 – 943.40 + 3,559.99 + 839.62 = 1,456.21
NPVa =  10,000 + (6,000 : 1.06^{3}) + (6,000 : 1.06^{4}) + (8,000 : 1.06^{5})
NPVa =  10,000 + 5,037.72 + 4,752.56 + 5,978.07 = 5,768.35
NPVb =  16,000 + (4,000 : 1.06) + (5,000 : 1.06^{2}) + (8,000 : 1.06^{3}) + (3,000 : 1.06^{4}) + (3,000 : 1.06^{5})
NPVb =  16,000 + 3,773.58 + 4,449.98 + 6,716.95 + 2,376.28 + 2,241.77 = 3,558.56
NPVi =  120,000 + (36,000 : 1.06) + (36,000 : 1.06^{2}) + (36,000 : 1.06^{3}) + (36,000 : 1.06^{4}) + (36,000 : 1.06^{5})
NPVi =  120,000 + 33,962.26 + 32,039.87 + 30,226.29 + 28,515.37 + 26,901.29 = 31,645.08
NPVb =  120,000 + (18,000 : 1.06) + (30,000 : 1.06^{2}) + (54,000 : 1.06^{3}) + (48,000 : 1.06^{4}) + (43,000 : 1.06^{5})
NPVb =  120,000 + 16,981.13 + 26,699.89 + 45,339.44 + 38,020.50 + 32,132.10 = 39,173.06
NPV =  290,000 + (120,000 : 1.06) + (132,000 : 1.06^{2}) + (145,000 : 1.06^{3}) + (160,000 : 1.06^{4})
NPV =  290,000 + 113,207.55 + 117,479.53 + 121,744.80 + 126,734.99 = 189,166.87
145,000        12m
38,000         x
x = 3.14 m
1m         30d
0.14m       x
x = 4.2 d
PB = 2 y, 3 m and 4 d
NPV =  15,000 + (3,600 : 1.06) + (6,600 : 1.06^{2}) + (6,600 : 1.06^{3}) + (6,600 : 1.06^{4}) + (6,600 : 1.06^{5}) + (6,600 : 1.06^{5})
NPV =  15,000 + 3,396.23 + 5,873.98 + 5,541.49 + 5,227.82 + 4,931.90 + 4,652.74 = 14,624.16
6,600         12m
4,800         x
x = 8.73m
1m          30d
0.73m        x
x = 21.9 d
PB = 2 y, 8 m and 22 d
NPVa =  10,000 + (3,000 : 1.1) + (5,000 : 1.1^{2}) + (8,000 : 1.1^{3})
NPVa =  10,000 + 2,727.27 + 4,132.23 + 6,010.52 = 2,870.02
NPVb =  9,000 + (7,000 : 1.1) + (6,000 : 1.1^{2}) + (1,000 : 1.1^{3})
NPVb =  9,000 + 6,363.64 + 4,958.68 + 751.31 = 3,073.63
NPV =  80 + (70 : 1.3) + (30 : 1.3^{2}) + (30 : 1.3^{3}) =  80 + 53.85 + 17.75 + 13.65 = 5.25
It's acceptable because the NPV is positive
NPV_{A} =  500 + (100 : 1.1) + (400 : 1.1^{3}) + (300 : 1.1^{4})
NPV_{A} =  500 + 90.91 + 300.53 + 204.90 = 96.34
NPV_{B} =  600 + (300 : 1.1) + (100 : 1.1^{2}) + (200 : 1.1^{3}) + (300 : 1.1^{4})
NPV_{B} =  600 + 272.73 + 82.64 + 150.26 + 204.90 = 110.53
PB_{1} = 2 y
PB_{2} = 1 y
NPV_{1} =  1,700 – (150 : 1.08) + (1,850 : 1.08^{2}) + (3,400 : 1.08^{3})
NPV_{1} =  1,700 – 138.89 + 1,586.08 + 2,699.03 = 2,446.22
NPV_{2} =  1,000 + (1,000 : 1.08) + (1,000 : 1.08^{2}) + (100 : 1.08^{3})
NPV_{2} =  1,000 + 925.93 + 857.34 + 79.38 = 862.65
PB_{A} = 2 y
PB_{B} = 3 y
NPV_{A} =  4,000 + (400 : 1.07) + (3,600 : 1.07^{2}) + (100 : 1.07^{3}) + (100 : 1.07^{4})
NPV_{A} =  4,000 + 373.83 + 3,144.38 + 81.63 + 76.29 =  323.87
NPV_{B} =  4,000 + (800 : 1.07) + (2,000 : 1.07^{2}) + (1,200 : 1.07^{3}) + (12,000 : 1.07^{4})
NPV_{B} =  4,000 + 747.66 + 1,746.88 + 979.56 + 9,154.74 = 8,628.84
NPV_{A} =  1,600 + (1,000 : 1.04) + (1,200 : 1.04^{2}) + (1,400 : 1.04^{3})
NPV_{A} =  1,600 + 961.54 + 1,109.47 + 1,244.59 = 1,715.6
NPV_{B} =  2,000 + (500 : 1.04) + (600 : 1.04^{2}) + (800 : 1.04^{3})
NPV_{B} =  2,000 + 480.77 + 554.73 + 711.20 =  253.3
NPV_{C} =  2,400 + (1,200 : 1.04) + (1,600 : 1.04^{2}) + (2,000 : 1.04^{3})
NPV_{C} =  2,400 + 1,153.85 + 1,479.29 + 1,777.99 = 2,011.13
PB_{A} = 1 y and y 6 m
PB_{B} = It isn't recovered
PB_{C} = 1 y and 9 m